正常椭球内部场的内蕴几何与密度分布  

Intrinsic Structure and Density of the Normal Ellipsoid's Interior

作　　者：黄金水[1] 

机构地区：[1]武汉测绘科技大学现代地球动力学实验室

出　　处：《武汉测绘科技大学学报》1997年第4期350-354,共5页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金

摘　　要：将重力场内蕴几何结构的研究引入到正常椭球内部场的研究中，深入探讨了内蕴几何量及其与内部物理量之间的关系，并据此建立了弱平衡条件下的基本微分方程，进而给出确定椭球内部内蕴几何量与场源密度分布的方法。研究表明，平衡形状理论中的Ｗａｖｒｅ公式和Ｃｌａｉｒａｕｔ方程可由内蕴几何与内部物理量之间的关系导出，它们是在平衡假设下取椭球近似的结果。In the paper,the intrinsic structure of the gravity field is first introduced into the study of the normal ellipsoid's interior.After the further relationship among the intrinsic geometric properties is built,the relation between the geometric properties and physics of the interior is presented,which follows,the basic differential equation on the condition of quasi equlibrium is set up,and finally the method to determine the intrinsic geometric poperties and density of the ellipsoid is given.It's shown that Wavre formula and Clairant equation which are on the condition of equilibrium and ellipsoidal approximation can also be derived in this way.

关 键 词：正常椭球 内蕴几何 密度分布 弱平衡条件 内部场 

分 类 号：P223[天文地球—大地测量学与测量工程]